(1) Field of the Invention
The invention described here provides a novel method of preventing the loss of focus and range of colors when digital image files are expanded to a larger size using existing methods of pixel interpolation. It also provides methods of selectively masking structural artifacts introduced by standard digital compression algorithms such as jpeg which defeat the most advanced Fourier transform based methods for expanding images to a larger size.
(2) Description of Prior Art
The challenge posed by the need to expand digital images without loss of image fidelity has prompted the development of several disparate systems for generating new pixels derived from information stored in the original pixels of an unexpanded image. The most widely used algorithms are polynomial interpolation equations that attempt to define values of new pixels by approximating the equations defining a surface in each color of the pixels as a function of position in the image. These algorithms use bilinear or bicubic equations to define a surface of best fit to the values of the original pixels. They suffer from the inevitable decay of edge focus and color intensity as they create an increasing population of pixels with color values intermediate to the original pixels during repeated rounds of image expansion. In contrast, the most successful and sophisticated methods could be characterized as pseudovectorizations. They use Fourier transforms to characterize the variations in color in the neighborhood of each pixel and then use those patterns to generate the intermediate pixels during image scale-up (U.S. Pat. No. 7,218,789; The contourlet transform: an efficient directional multiresolution image representation IEEE Transactions on Image Processing Volume: 14, Issue: 12 pp 2091-2106). These methods works considerably better than the aforementioned polynomial interpolations because 1) they are much more sensitive to complex structural variation in the data; and 2) Because random noise in images tends to be high frequency data with a low autocorrelation coefficient, and Fourier transforms are the most efficient way known to suppress such noise. Thus, the most successful previous attempts at solving these problems have focused on using Fourier transform techniques to characterize functions closely approximating the color variations among pixels adjacent to and at identified edges, then using those functions to properly color the new, initially blank pixels in an expanded image file. These methods have achieved significant advances over systems that average color difference between pixels using interpolation algorithms such as simple spline approximations or the bicubic algorithm, but they suffer from a different basic limitation. In small digital image files complex shapes are crudely sampled, leading to sharply defined anomalies known as sampling artifacts; or, alternatively, lossy compression systems, such as the widely used jpeg algorithms, will create structures, compression artifacts, such as strong edged square tiling that are difficult to logically distinguish from the true edges of the original image. Algorithms that are optimized to retain the color differences among pixels rather than averaging the differences, such as the Fourier transform based algorithms, will frequently maintain and strengthen these artifacts, thereby severely limiting the degree to which the images can be expanded before the artifacts make them esthetically and commercially unacceptable.